A rectangular coil $20\,cm \times 20\,cm$ has $100$ $turns$ and carries a current of $1\, A$. It is placed in a uniform magnetic field $B =0.5\, T$ with the direction of magnetic field parallel to the plane of the coil. The magnitude of the torque required to hold this coil in this position is........$N-m$

Define $\mathrm{SI}$ unit of electric charge in terms of Ampere.

Suppose an isolated north pole is kept at the centre of a circular loop carrying a electric current $i$. The magnetic field due to the north pole at a point on the periphery of the wire is $B$. The radius of the loop is $a$. The force on the wire is

A square-shaped conducting wire loop of dimension moving parallel to the $X$-axis approaches a square region of size $b(a < b)$, where a uniform magnetic field $B$ exists pointing into the plane of the paper (see figure). As the loop passes through this region, the plot correctly depicting its speed $v$ as a function of $x$ is

A straight rod of mass $m$ and length $L$ is suspended from the identical spring as shown in the figure. The spring stretched by a distance of $x_0$ due to the weight of the wire. The circuit has total resistance $R\Omega$ . When the magnetic field perpendicular to the plane of the paper is switched on, springs are observed to extend further by the same distance. The magnetic field strength is 

The force exerted by a magnetic field on a wire having length $L$ and current $I$ is perpendicular to the wire and given as $\left| F \right| = IL\left| B \right|$ . An experimental plot shows $(\vec F)$ as function of $L$ . The plot is a straight line with a slope $S = \left( {10 \pm 1} \right) \times {10^{ - 5}}\ AT$. The current in the wire is $\left( {15 \pm 1} \right)\ mA$ . The percentage error in $B$ is